Question

NO SPAM ..NO PLAGIARISM..
DEEP EXPLANATION NEEDED..​

Answer 1

Step-by-step explanation:

let secx + tanx = t

differentiation w r t x

→ sec²x + secx tanx = dt/dx

→ secx(secx + tanx) = dt/dx

→ secx(t) = dt/dx

→secx.dx = 1/t.dt ________ eq 1

Now according to the question we have

(secx)

integration of ____________.dx

(secx + tanx)

replacing value according to eq 1

→ ! 1/(t⁹'²).1/t.dt

→ ! 1/t¹¹'².dt

→ ! (t)-¹¹'².dt

→ [(t)-⁹'² ]/(-9/2) + c

→ -2/9(secx + tanx) + c

here this " ! " symbol I have used for integration